Answer:
The maximum house value you could afford with a 30-year loan of $1947.33 per month at 3% interest compounded monthly is $428,633.54.
Explanation:
To calculate the maximum house value you could afford with a 30-year loan of $1947.33 per month at 3% interest compounded monthly, we can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r/n)^(-nt)) / (r/n)],
where:
PV = present value of the loan (maximum house value you could afford)
PMT = monthly payment ($1947.33 in this case)
r = annual interest rate (3% in this case)
n = number of compounding periods per year (12 for monthly compounding)
t = total number of payments (30 years x 12 months per year = 360 payments)
Substituting the values given, we get:
PV = $1947.33 x [(1 - (1 + 0.03/12)^(-12*30)) / (0.03/12)]
PV = $428,633.54 (rounded to the nearest cent)
Therefore, the maximum house value you could afford with a 30-year loan of $1947.33 per month at 3% interest compounded monthly is $428,633.54.